Calculator with LOTS of decimals

  • Context: High School 
  • Thread starter Thread starter Usaf Moji
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Discussion Overview

The discussion revolves around the need for calculators or software capable of performing calculations with high precision, particularly when dealing with numbers that have significant differences in their orders of magnitude. Participants share their experiences and recommendations for tools that can avoid unwanted rounding errors in such calculations.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant expresses frustration with existing calculators that round off answers too much, specifically when calculating expressions like 4.5 x 10-12 - (4.5 x 10-12 - 9.2 x 10-30).
  • Another participant suggests that most scientific calculators can provide the correct answer if the exponential button is used.
  • A participant mentions that the Windows calculator can handle the calculations needed.
  • One user recommends using PARI, a number theory package, which can provide up to 28 decimal places and offers a command to set precision to a much higher number, although it may still produce slightly inaccurate results in some cases.
  • Another participant supports the recommendation of PARI and provides examples demonstrating its precision capabilities, including calculations with extremely small numbers.

Areas of Agreement / Disagreement

Participants generally agree that certain calculators and software can perform the required calculations, but there is no consensus on which tool is definitively the best, as different tools may yield slightly different results.

Contextual Notes

Some limitations are noted regarding the precision of calculations in different tools, with specific examples showing that even high-precision tools can produce results that are not entirely accurate under certain conditions.

Usaf Moji
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Hi, I'm trying to do some caculations involving numbers with big differences in their orders of magnitude. Unfortunately, all the cacluclating tools I can find always round off the answers too much to be of any use to me.

For example, if I type 4.5 x 10-12 - (4.5 x 10-12 - 9.2 x 10 -30) I want a calculator that will give me 9.2 x 10 -30. But all the calculators I've used give me 0 due to unwanted rounding during the calculation. Even Python does this.

Does anyone know where I could get a calculator or program that can do the calculation I need? I would prefer something with a simple interface resembling a hand-held calculator (like what Python uses) rather than something that requires any kind of programming.

Thanks.
 
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I think most scientific calculators will give you that answer assuming that you use the exp. button.
 
Usaf Moji said:
Hi, I'm trying to do some caculations involving numbers with big differences in their orders of magnitude. Unfortunately, all the cacluclating tools I can find always round off the answers too much to be of any use to me.

For example, if I type 4.5 x 10-12 - (4.5 x 10-12 - 9.2 x 10 -30) I want a calculator that will give me 9.2 x 10 -30. But all the calculators I've used give me 0 due to unwanted rounding during the calculation. Even Python does this.

Does anyone know where I could get a calculator or program that can do the calculation I need? I would prefer something with a simple interface resembling a hand-held calculator (like what Python uses) rather than something that requires any kind of programming.

Thanks.

The calculator that comes with Windows can do it.

CS
 
stewartcs said:
The calculator that comes with Windows can do it.

CS

Hey, you're right! Thanks!
 
You can use, for free, PARI, the package for number theory. Just look it up on the internet. Normally the program I use goes to 28 decimal places. A little secret here, found in the tutorial is to use \pX to get X places of precision. You can set that for X=50, or X=500 for that matter.

However in the example you gave, depending upon the brackets, it sometimes insists on giving 9.1 followed by a long string of 9s. Even for 500 places its off at the last 7 giving 615927*10^-30.
 
I second the Pari recommendation.

Code: 
(15:02)(1+1e-20)^2-1-2e-20
%5 = 9.99999984 E-41

Code: 
(15:02)\p 1000
   realprecision = 1001 significant digits (1000 digits displayed)
(15:02)(1+1e-400)^2-1-2e-400
%6 = 9.9999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999999999999999999999999999999999999
99999999999999999999999999999999999999999999999526402 E-801
 

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